Alonso-Marroquin Fernando, Huang Pengyu, Hanaor Dorian A H, Flores-Johnson E A, Proust Gwénaëlle, Gan Yixiang, Shen Luming
School of Civil Engineering, The University of Sydney, Sydney, New South Wales 2006, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Sep;92(3):032405. doi: 10.1103/PhysRevE.92.032405. Epub 2015 Sep 17.
Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.
通过基于球多边形的模拟和接触斜率分析，我们研究了表面形貌和原子尺度摩擦对具有分形表面结构的刚性块体之间宏观观测到的摩擦的影响。从我们的数学推导可知，宏观摩擦角是原子摩擦角与接触表面之间斜率角之和的结果。后者是通过一个替代特征函数确定两个表面轮廓之间所有可能的接触斜率而得到的。我们的理论通过具有分形科赫表面的球多边形的数值模拟得到验证，并应用于描述魏尔斯特拉斯 - 曼德勃罗特表面的摩擦特性。模拟与理论之间的一致性表明，为了解释宏观摩擦行为，表面形态的描述符应从特征函数而非接触表面的斜率来定义。
